Multiple Time-scale Model Research Articles

Sensitivity analysis of multiple time-scale building energy using Bayesian adaptive spline surfaces

Sensitivity analysis has been widely used in building energy analysis to identify key variables influencing building energy and carbon emissions. However, most previous studies only focus on the single time scale energy use of buildings when conducting sensitivity analysis. The multiple time-scale sensitivity analysis would lead to increased complexity and challenges in building energy analysis. This paper proposes a new systematical procedure for global variance-based sensitivity analysis of multiple time-scale energy use of buildings. A case study of an office building is used to demonstrate the application of this approach using the Bayesian adaptive spline surface (BASS) models at three different time scales (annual, monthly, and daily). The results indicate that the procedure proposed here can provide fast and reliable sensitivity results for the multiple time-scale building energy assessment. The BASS learning models have the advantages of high predictive performance and the fast computation of sensitivity indicators in a closed form without Monte Carlo integrals. The application of principal component analysis can deal with the highly correlated multi-output energy use at a smaller time scale, which can further reduce computational costs. Moreover, the sensitivity analysis at the different time scales can provide new insights into energy characteristics due to the intrinsic variations of weather conditions. This systematical procedure can provide useful guidance for the multiple time-scale model calibration and multi-step ahead predictions of buildings. Moreover, the method proposed here can be extended to the sensitivity analysis of energy use in different time scales (sub-hourly, hourly, or daily) for other energy systems (such as PV, solar thermal, and wind).

Autism detection based on multiple time scale model

Objective. Current autism clinical detection relies on doctor observation and filling of clinical scales, which is subjective and prone to misdetection. Existing autism research of functional magnetic resonance imaging (fMRI) over-compresses the time-scale information and has poor generalization ability. This study extracts multiple time scale brain features of fMRI, providing objective detection. Approach. We first use least absolute shrinkage and selection operator to build a sparse network and extract features with a time scale of 1. Then, we use hidden markov model to extract features that describe the dynamic changes of the brain, with a time scale of 2. Additionally, to analyze the features of the potential network activity of autism from a higher time scale, we use long short-term memory to construct an auto-encoder to re-encode the original data and extract the features at a higher time scale, with a time scale of T, and T is the time length of fMRI. We use recursive feature elimination for feature selection for three different time scale features, merge them into multiple time scale features, and finally use one-dimensional convolution neural network for classification. Main results. Compared with well-established models, our method has achieved better results. The accuracy of our method is 76.0%, and the area under the roc curve is 0.83, tested on completely independent data, so our method has better generalization ability. Significance. This research analyzes fMRI sequences from multiple time scale to detect autism, and it also provides a new framework and research ideas for subsequent fMRI analysis.

Geometric Singular Perturbation Analysis of a Multiple Time-scale Model for Diabetes and COVID-19 Comorbidity

More and more information on mortality and morbidity indicates that in order to fight the COVID-19 pandemic, it is important to focus our attention on comorbidities. Several reports evidence of how many elderly patients who become severely ill exhibit underlying illness such as cardiovascular disease, kidney disease, tumor, and more to our special attention here, type 2 diabetes. Better understanding of the mechanism underlying the comorbidity between different diseases requires merging models of systems across different time-scales. The model homogenization across multiple spatial and time scales poses an important challenge to researchers in the field of medical science. An approach that has been found relatively efficient in the analysis of such models is the use of singular perturbation technique. Here, we study a differential equation model system with multiple time scales which describes the diabetes and COVID-19 comorbidity. It tracks the changes in levels of plasma glucose, insulin, and functional-cells, incorporating insulin resistance and inflammation responses. The model is analyzed with the geometric singular perturbation technique, by which conditions on the system parameters may be derived to identify regions in which the system exhibits different dynamic behavior, whether the system would be stable, or eventually oscillate in a sustained fashion. Discussion of these conditions allows us to better understand how comorbidity mediates the development of life-threatening symptoms in a diabetic patient in order that proper care and treatment may be prescribed.

Classification of bursting patterns: A tale of two ducks.

Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active research since the early 1980s and is still ongoing. As a by-product, it establishes analytical and numerical foundations for studying complex temporal behaviors in multiple timescale models of cellular activity. In this review, we first present the seminal works of Rinzel and Izhikevich in classifying bursting patterns of excitable systems. We recall a complementary mathematical classification approach by Bertram and colleagues, and then by Golubitsky and colleagues, which, together with the Rinzel-Izhikevich proposals, provide the state-of-the-art foundations to these classifications. Beyond classical approaches, we review a recent bursting example that falls outside the previous classification systems. Generalizing this example leads us to propose an extended classification, which requires the analysis of both fast and slow subsystems of an underlying slow-fast model and allows the dissection of a larger class of bursters. Namely, we provide a general framework for bursting systems with both subthreshold and superthreshold oscillations. A new class of bursters with at least 2 slow variables is then added, which we denote folded-node bursters, to convey the idea that the bursts are initiated or annihilated via a folded-node singularity. Key to this mechanism are so-called canard or duck orbits, organizing the underpinning excitability structure. We describe the 2 main families of folded-node bursters, depending upon the phase (active/spiking or silent/nonspiking) of the bursting cycle during which folded-node dynamics occurs. We classify both families and give examples of minimal systems displaying these novel bursting patterns. Finally, we provide a biophysical example by reinterpreting a generic conductance-based episodic burster as a folded-node burster, showing that the associated framework can explain its subthreshold oscillations over a larger parameter region than the fast subsystem approach.

Multifractality in a nested velocity gradient model for intermittent turbulence

Small scale intermittency is ubiquitous in turbulent flows. Many features of small-scale motions can be described by the velocity gradient tensor (VGT) for which the nonlinear term in the Navier-Stokes equations (NSE) is a source of strong fluctuations. The figure shows intermittent time signals of longitudinal VGT elements along Lagrangian trajectories from five levels of a recently proposed nested multiple time-scale model (MTSM), partly derived from NSE. We show that a single level of MTSM valid at moderate Reynolds numbers (Re) can generate valid statistics and scaling exponents for arbitrarily high Re. Excellent agreement with direct numerical simulation and experimental data is found.

Dynamic characteristics of proton exchange membrane fuel cell on a multiple time scale

The current research on the dynamic performance of the proton exchange fuel cell is mostly aimed at the influence of operating parameters on the system, but does not involve with the dynamic characteristics of the cell on a multiple time scale nor the study of the corresponding multiple time scale model. In order to detect the dynamic changes of the proton exchange membrane fuel cell, the effects of various factors in the system on the output performance on different time scales are investigated. The effective partial pressure of oxygen and hydrogen are obtained by the mass diffusion equation and the ideal gas state equation, and the dynamic model is established according to the law of conservation of energy, the law of thermodynamics, and the electrochemical reaction equation. By setting the load mutations with a large/medium/small time scale dynamic duration of 0.6 s, 165 s, and16 min, respectively, the mechanism with which voltage suddenly changes when the load current changes abruptly is studied. Starting from the long time constant during which the dynamic performance takes effect, the control variable is used to analyze the double-layer charge. The influences of layer effect capacitance <i>C</i>, fuel oxidant delay time constant <i>τ</i><sub>e</sub>, and thermodynamic characteristics (temperature <i>T</i>) on the dynamic performance ( initial values of variables: <i>C</i> = 4 F, <i>τ</i><sub>e</sub> = 80 s, and <i>T</i> = 307.7 K) clarify the action intensities on different time scales. With the help of Matlab/Sumlink platform the simulation results are obtained and the correctness and effectiveness of the built model are verified. The simulation results show that the sudden change in voltage is due to the open circuit voltage and Ohmic polarization resistance, and the Ohmic resistance is dominant (the Ohmic overvoltage change value is 2 V, and the open circuit voltage change is 0.05 V), and the <i>C</i> pair dynamics on a small time scale (ms). The performance plays a leading role. Specifically, <i>τ</i><sub>e</sub> has a greater effect on the dynamic characteristics on a medium time scale (s), and <i>T</i> has a stronger effect on a large time scale (10<sup>2</sup>–10<sup>3</sup> s). Based on the above deduction, a multi-time scale model of the battery is derived. The research provides the reference and theoretical support for subsequent battery energy management, evaluation of dynamic performance, and precise control.

Multi-Timescale Wavelet Scattering With Genetic Algorithm Feature Selection for Acoustic Scene Classification

In this paper, we apply a genetic algorithm (GA) for feature selection, wrapper approach, on wavelet scattering (WS) second-order coefficients to reduce the large frequency dimension (>500). The evaluation demonstrates the capability of GA to reduce the dimension space by approximately 30% while ensuring a minimum performance drop. Furthermore, the reduced WS directly impacts the training time of the convolutional neural network, by reducing the computational time by 20% to 32%. The paper extends its scopes to explore GA for feature selection on multiple timescales of WS: 46ms, 92ms, 185ms, and 371ms. Incorporating multiple timescales has improved classification performance (by ~ around 2.5%) as an acoustic representation usually contains information at different time scales. However, it can increase computational cost due to the larger frequency dimension of 1851. With the application of GA for feature selection, the frequency dimension is reduced by 50%, saving around 40% computational time, thus increasing the classification performance by 3% compared to a vanilla WS. Lastly, the entire implementations are evaluated using the Detection and Classification of Acoustic Scenes and Events (DCASE) 2020 dataset, and the proposed multiple timescales model achieves 73.32% of classification accuracy.

A new hybrid modeling and optimization algorithm for improving carbon efficiency based on different time scales in sintering process

Sintering process is a major energy-consumption process in steel making processes. Carbon efficiency, which reflects the level of the energy-consumption, is affected by the raw material variables and the operating variables. This situation makes the process with special dynamic characteristics, especially with different operation periods. However, there is seldom research on carbon efficiency with the multiple time-scale property taken into account. This paper introduces an optimization method for carbon efficiency based on an intelligent multiple time-scale model, which is able to optimize process variables in both long and short time scales. As the comprehensive carbon ratio (CCR) and the ratio between CO and CO2 in exhaust gas (CO/CO2) are taken as the carbon efficiency indexes, a predictive model consisting of two sub-models is developed, one for predicting the state variables with a single neural network (NN), and the other for predicting carbon efficiency indexes with a linear combination of NNs. Then a multi-objective, multi-time-scale optimization framework is designed, which is able to optimize carbon efficiency in two time scales, according to the optimization variables available encountered at different operation periods. Finally, the experimental results based on actual process data shows its feasibility and improvement in carbon efficiency optimization.

Retraction Note to: A joint model for analyzing topic and sentiment dynamics from large-scale online news

Many of today’s online news websites and aggregator apps have enabled users to publish their opinions without respect to time and place. Existing works on topic-based sentiment analysis of product reviews cannot be applied to online news directly because of the following two reasons: (1) The dynamic nature of news streams require the topic and sentiment analysis model also to be dynamically updated. (2) The user interactions among news comments can easily lead to inaccurate topic extraction and sentiment classification. In this paper, we propose a novel probabilistic generative model (DTSA) to extract topics and the specified sentiments from news streams and analyze their evolution over time simultaneously. In DTSA, three different timescale models are studied to account for the historical dependencies of sentiment-topic word distributions at current epoch, continuous, skip and multiple timescale models. Additionally, we further consider the links among news comments to avoid the error caused by user interactions. In order to mine more interpretable topics, a Conditional Random Fields (CRF) model is adopted to label a set of meaningful phrases for augmenting the bag-of-word features. Finally, we derive distributed online inference procedures to update the model with newly arrived data and show the effectiveness of our proposed model on real-world data sets.

A CFD hybrid approach to simulate liquid-phase chemical reactors

Design and safety assessments of chemical reactors can be done using Reynolds Averaged Navier-Stokes (RANS) type equations. The averaging procedure of transport equations gives rise to unclosed terms, which must be properly modeled independently on the computational cell size. In particular, presence of chemical reactions leads to an additional source term in species equation. The averaged value of this term involves effects of both chemical kinetics and turbulence. Turbulence-kinetics interaction (TKI) models must be then developed in order to close species transport equations, so that Computational Fluid Dynamics (CFD) can be used to reduce the number of experiments required to design a chemical reactor.Many TKI models have been developed in the past, mainly for gaseous systems, while liquid-phase models have been less investigated because of demanding theoretical challenges. Therefore, the purpose of this work is the development of a new TKI model for liquid phase reactions, which combines the Laminar Rate model (for kinetic controlled systems) with the Multiple Time Scales model (for turbulence controlled systems) allowing its use also when kinetic and turbulent mixing characteristic times are comparable. An analysis of the influence of the turbulence model coupled with the proposed model was carried out to identify the most suitable turbulence model, and two different case studies were investigated to show the potentialities of the proposed approach.

Singular perturbation analysis of a two-site model for an epidemic in age-structured population

We formulate a model describing the dynamics for the spatial propagation of an SIS epidemic within a population, with age structure, living in an environment divided into two sites. An analysis of the model is given. We prove the existence of a unique disease free equilibrium (DFE) and its (local and global) stability. Further, we assume that fast infection processes and fast migration processes take place in the above-mentioned model; i.e. such processes last only a few days (less than a week). In opposition to such processes, demographic processes such as birth, death and maturation last quite a lot of years. Such a gap between the time scales gives rise to a multiple time scales model, in particular a singularly perturbed model. Through a singular perturbation analysis, based on Tikhonov theorem, we prove that for certain classes of initial conditions the nonlinear perturbed model can be approximated with very good accuracy by lower-dimensional linear models.

Unifying practice schedules in the timescales of motor learning and performance

In this article, we elaborate from a multiple time scales model of motor learning to examine the independent and integrated effects of massed and distributed practice schedules within- and between-sessions on the persistent (learning) and transient (warm-up, fatigue) processes of performance change. The timescales framework reveals the influence of practice distribution on four learning-related processes: the persistent processes of learning and forgetting, and the transient processes of warm-up decrement and fatigue. The superposition of the different processes of practice leads to a unified set of effects for massed and distributed practice within- and between-sessions in learning motor tasks. This analysis of the interaction between the duration of the interval of practice trials or sessions and parameters of the introduced time scale model captures the unified influence of the between trial and session scheduling of practice on learning and performance. It provides a starting point for new theoretically based hypotheses, and the scheduling of practice that minimizes the negative effects of warm-up decrement, fatigue and forgetting while exploiting the positive effects of learning and retention.

RETRACTED ARTICLE: A joint model for analyzing topic and sentiment dynamics from large-scale online news

Many of today’s online news websites and aggregator apps have enabled users to publish their opinions without respect to time and place. Existing works on topic-based sentiment analysis of product reviews cannot be applied to online news directly because of the following two reasons: (1) The dynamic nature of news streams require the topic and sentiment analysis model also to be dynamically updated. (2) The user interactions among news comments can easily lead to inaccurate topic extraction and sentiment classification. In this paper, we propose a novel probabilistic generative model (DTSA) to extract topics and the specified sentiments from news streams and analyze their evolution over time simultaneously. In DTSA, three different timescale models are studied to account for the historical dependencies of sentiment-topic word distributions at current epoch, continuous, skip and multiple timescale models. Additionally, we further consider the links among news comments to avoid the error caused by user interactions. In order to mine more interpretable topics, a Conditional Random Fields (CRF) model is adopted to label a set of meaningful phrases for augmenting the bag-of-word features. Finally, we derive distributed online inference procedures to update the model with newly arrived data and show the effectiveness of our proposed model on real-world data sets.

Multiple Time Scale Models in Sport and Exercise Science

ABSTRACTIn sport and exercise research, examining both within- and between-individual variation is crucial. The ability to investigate change both within competitive events and across a competitive season is a priority for many sport researchers. The aim of this article is to demonstrate an approach to analyzing intensive longitudinal data collected through time-scale-dependent longitudinal designs. Following didactic presentation of the approach, two illustrations from secondary data analysis are used to describe the modeling process in detail. Illustration 1 includes affective response data from an exercise intervention randomized pilot study. Illustration 2 uses referee and player distance data collected during professional soccer games in the English Premier League. Each illustration describes a process for testing and comparing multiple time scale models based on the three-level multilevel model, and results are interpreted. In the discussion, advantages and limitations of the approach are highlighted.

Using multiple timescale models for the evaluation of a time-dependent treatment.

In survival analysis, the absolute measure of cumulative risk provided by the Kaplan-Meier estimator is still the most used quantity for its easy calculation and direct interpretability. However, for describing the survival after an intervention that may occur at different times from baseline observation, the Kaplan-Meier estimator generally yields to biased results if intervention is considered as fixed at baseline. The main focus of the present paper is to extend the use of a multiple timescale model in the presence of a time dependent intervention. The aim is to obtain 1) an estimate of treatment effect in terms of hazard ratios by flexible modeling, 2) a valid prediction tool, i.e. estimate of prognosis for a patient who changes treatment later in time, and 3) an appropriate graphical representation of survival in the presence of a time dependent treatment change, accounting for different timescales. We will show the advantages of this approach on the comparison of chemotherapy versus transplant in children with high-risk acute lymphoblastic leukemia in first remission. We considered a model with two timescales that accounts for the change in treatment at different times in the disease course. An alternative approach to survival estimates is also proposed which has some advantages over the traditional landmark approach: it uses all the data available to plot survival from the date of remission, it avoids the arbitrary choice of a landmark time and explicitly models the change in hazard due to transplant.

A singularly perturbed age structured SIRS model with fast recovery

Age structure of a population often plays a significant role in the spreading of a disease among its members. For instance, childhood diseases mostly affect the juvenile part of the population, while sexually transmitted diseases spread mostly among the adults. Thus, it is important to build epidemiological models which incorporate the demography of the affected populations. Doing this we must be careful as many diseases act on a time scale different from that of the vital processes. For many diseases, e.g. measles, influenza, the typical time unit is one day or one week, whereas the proper time unit for the vital processes is the average lifespan in the population; that is, 10-100 years. In such a case, the epidemiological model with vital dynamics becomes a multiple time scale model and thus it often can be significantly simplified by various asymptotic methods. The presented paper is concerned with an SIRS type disease spreading in a population with a continuous age structure modelled by the McKendrick-von Foerster equation. We consider a disease with a quick recovery rate in a large population. Though it is not too surprising that in such a model the introduced disease quickly vanishes, the result is mathematically interesting as the error estimates are uniform on the whole infinite time interval, in contrast to the typical results based on the Tikhonov theorem and classical asymptotic expansions.

Analysis of the factors influencing information transmission at the calyx of Held

The calyx of Held is a giant glutamatergic synapse located in the medial nucleus of the trapezoid body (MNTB) of the mammalian auditory brainstem. It is an important model system for studying short-term plasticity because each postsynaptic MNTB neuron receives only one giant synapse, and it is possible to record both pre- and postsynaptic events simultaneously. Physiological experiments show that the evoked excitatory postsynaptic current (EPSC) from the calyx displays a significant depression in response amplitude during a sustained stimulus train [1]. This observation is the result of interactions between various pre- and postsynaptic components occurring across multiple time-scales. Hundreds of readily releasable vesicles (RRVP) aggregate at the different active zones on the presynaptic terminal. The stochastic release of neurotransmitter from the RRVPs (triggered by influx of calcium ions during action potentials, APs), can exhaust the supply of vesicles. Simultaneously, the depleted RRVPs are constantly replenished by a large vesicle reserve pool, and this replenishment is also enhanced by a calcium-dependent process (mediated by the presynaptic APs). The amplitude of the presynaptic AP-evoked calcium ion concentration is affected by inactivation and facilitation of voltage-gated calcium channels as well as activation of presynaptic metabotropic glutamate receptors (mGluRs). In this study we extend our deterministic, multiple time-scale model of the calyx of Held [2,3] to a stochastic version. We use information theory to measure the amount of information transmitted between pre- and postsynaptic compartments [4]. A series of long, homogeneous Poisson spike trains with mean frequencies up to several hundred Hertz are used to stimulate the calyx model. This spike train is repeated many times, allowing the calculation of the conditional and unconditional entropy of the postsynaptic EPSC amplitude in response to presynaptic interspike intervals (ISI). The mutual information, a measure of the information content of the postsynaptic response (EPSC) about the afferent spike train (ISI), is then computed in terms of conditional and unconditional entropies. The results show that the information content in the postsynaptic response is influenced by the degree of variation of presynaptic calcium ion concentration. Rapid onset and recovery from facilitation maintains high information transfer rates across the frequency range. Suppression of calcium transients by slowly recovering inactivation and mGluR activation results in less information transmission, but prevents depletion of the RRVPs. Fast-acting postsynaptic receptor desensitisation also contributes to information transmission, but in a competitive way to facilitation.

A versatile model for TCP bandwidth sharing in networks with heterogeneous users

Enabled by the emergence of various access technologies (such as ADSL and wireless LAN), the number of users with high-speed access to the Internet is growing rapidly, and their expectation with respect to the quality-of-service of the applications has been increasing accordingly. With TCP being the ubiquitous underlying end-to-end control, this motivates the interest in easy-to-evaluate, yet accurate, performance models for a TCP-based network shared by multiple classes of users. Building on the vast body of existing models, we develop a novel versatile model that explicitly captures user heterogeneity, and takes into consideration dynamics at both the packet level and the flow level. It is described as to how the resulting multiple time-scale model can be numerically evaluated. Validation is done by using NS2 simulations as a benchmark. In extensive numerical experiments, we study the impact of heterogeneity in the round-trip times on user-level characteristics such as throughputs and flow transmission times, thus quantifying the resulting bias. We also investigate to what extent this bias is affected by the networks’ ‘packet-level parameters’, such as buffer sizes. We conclude by extending the single-link model in a straightforward way to a general network setting. Also in this network setting the impact of heterogeneity in round-trip times is numerically assessed.

How can we bridge the multiple timescale models of radiation damage processes?

Recent modeling efforts on the radiation damage over multi-time scales are summarized. Under irradiation, materials experience multiple physical processes such as collision, cooling, thermalization and diffusions that extend over vast range of temporal scales. Correspondingly, modeling of these processes requires different schemes efficient for evaluation on each scale. The main outcome of individual process is obtained by utilizing the various methods, such as binary collision approximation, molecular dynamics, kinetic Monte Carlo, and rate theory. The remaining key issue to overcome is how to establish a methodology for passing information between the models and how to maintain the physical consistency.

A PDF propagation approach to model turbulent dispersion in swirling flows

A computationally efficient approach that solves for the spatial covariance matrix along the dense particle ensemble-averaged trajectory has been successfully applied to describe turbulent dispersion in swirling flows. The procedure to solve for the spatial covariance matrix is based on turbulence isotropy assumption, and it is analogous to Taylor's approach for turbulent dispersion. Unlike stochastic dispersion models, this approach does not involve computing a large number of individual particle trajectories in order to adequately represent the particle phase; a few representative particle ensembles are sufficient to describe turbulent dispersion. The particle Lagrangian properties required in this method are based on a previous study (Shirolkar and McQuay, 1998). The fluid phase information available from practical turbulence models is sufficient to estimate the time and length scales in the model. In this study, two different turbulence models are used to solve for the fluid phase – the standard k– ε model, and a multiple-time-scale (MTS) model. The models developed here are evaluated with the experiments of Sommerfeld and Qiu (1991). A direct comparison between the dispersion model developed in this study and a stochastic dispersion model based on the eddy lifetime concept is also provided. Estimates for the Reynolds stresses required in the stochastic model are obtained from a set of second-order algebraic relations. The results presented in the study demonstrate the computational efficiency of the present dispersion modeling approach. The results also show that the MTS model provides improved single-phase results in comparison to the k– ε model. The particle statistics, which are computed based on the fundamentals of the present approach, compare favorably with the experimental data. Furthermore, these statistics closely compare to those obtained using a stochastic dispersion model. Finally, the results indicate that the particle predictions are relatively unaffected by whether the Reynolds stresses are based on algebraic relations or on the turbulence isotropy assumption.